keras ValueError: Error when checking model target: expected activation_4 to have shape (None, 19) but got array with shape (100, 1)
Try to use the model like this, for example:

model = Sequential() 
model.add(Dense(50, input_shape=(2,))) 
model.add(Activation("relu")) 
model.add(Dense(50, activation='softmax')) 
model.add(Dense(1, activation='linear')) 
model.compile(optimizer='sgd', loss='mse', metrics=["accuracy"])



This means that first layer will have 50 neurons and can receive data in form of matrix with 2 columns and an unspecified number of rows.
So you can prepare your data in this form – 2 numbers for adding in each row.

Dense(50, input_shape=(2,))



At the end, you need a layer with 1 neuron and the 'linear' activation, because you expect one simple number as a result.

Dense(1, activation='linear')



And finally, use 'mse' loss function or something similar. 'categorical_crossentropy' is needed for classification tasks, not regression as needed for you.
See: https://keras.io/objectives/